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2 years ago

Rewrite the expression with positive exponents (problem #4)

Mathematics

1 answer:

Anestetic [448]2 years ago

7 0

Having a negative exponent is the same as have the inverse of the exponent

x⁻² = 1 / x²

Plugging in the Numbers,

(12a^3b^-4)/ (4a^-2b)

This is the Answer

12a^3(4a^2)/(3b^5)

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Question 2(Multiple Choice Worth 5 points) (04.01)The Boardman family walked two over five of a mile in two over seven of an hou

Zolol [24]

Answer:

The unit rate in miles per hour = <em>1.4 miles/hr</em>

Step-by-step explanation:

Given that:

Distance walked by Boardman family = Two over five of a mile = $\frac{2}{5}\ miles$

Time taken by Boardman family = Two over seven of an hour = $\frac{2}{7}\ hour$

To find:

The unit rate in the miles per hour = ?

Solution:

Formula for the rate or the speed can be given as:

$Speed = \dfrac{Distance}{Time}$

Putting the values:

$\Rightarrow \dfrac{\frac{2}5}{\frac{2}7}\\\Rightarrow \dfrac{7}{5}\\\Rightarrow \bold{1.4\ miles/hr}$

So, the unit rate in miles per hour = <em>1.4 miles/hr</em>

4 0

2 years ago

Please solve quickly

solong [7]

Answer:

24.9π

Step-by-step explanation:

Curcle Area=πR^2

A= πR^2 × 140°/360°

A= π×8^2 × 0.389 =~ 78.15

4 0

1 year ago

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

VikaD [51]

Complete Question

The complete question is shown on the first uploaded image

Answer:

$P(X = 8) = 0.0037$

$P(X < 5) = 0.805$

$P(X > 6) = 0.0206$

I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is $p = 0.267$

Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable X we have that

$X \ \ \~ \ \ { B ( p , n )}$

The probability distribution function for binomial distribution is

$P(X = x ) = ^nC_x * p^x * (1 -p) ^{n-x}$

Considering question a

Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as

$P(X = 8) = ^{12} C_8 * (0.267)^8 * (1- 0.267)^{12-8}$

Here C denotes combination

$P(X = 8) = 495 * 0.000025828 * 0.28867947$

$P(X = 8) = 0.0037$

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as

$P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)]$

=> $P(X < 5 ) =[ ^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0} + \cdots + ^{12} C_4 * (0.267)^4 * (1- 0.267)^{12-4} ]$

=> $P(X < 5 ) = 0.02406 + 0.10516 + 0.21067 + 0.25580 + 0.20964$

=> $P(X < 5) = 0.805$

Considering question c

Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

$P(X > 6) = 1 - p(X \le 6)$